Finding a good hotel in Damascus is easy. But finding a bad one is easy too! Tourism was quite well-developed in Syria in the 2000s, and many hotels have miraculously made it through the crisis years without a scratch – but many are in need of renovation and investment, so it's worth doing some research into which one best fits your budget, comfort requirements, and mood.

Hotels often quote their rates and accept payment in US dollars but naturally take Syrian pounds too, though you may need a small wheelbarrow to pay for your stay. Euros are often also accepted at the rate of the day; it's good to check this in advance if you're only carrying this currency. Credit card payments are currently only possible in the most upmarket hotels. Damascus hotels are known to be open to bargaining, so if you have a good proposition for a lower price, perhaps in combination with a longer stay, by all means see if the hotel agrees. 

Traveller numbers are still very modest, so away from the high-end hotels that may be booked out by international organisations, it’s often perfectly feasible to arrive without a reservation and simply compare a few mid-range places to see if the price and mood fit your expectations. 
If you’re visiting in winter, keep in mind that heating and insulation are often problematic in budget at some mid-range accommodation options – check in advance that the heating and hot water work. If this all fails, hotels are usually happy to provide extra blankets. 
Regulations forbid unmarried couples from sharing a hotel room without providing a marriage certificate, but foreigners are usually exempt from this rule. 
A word on brands – seeing brand names like Four Seasons or Sheraton on hotel facades in Syria does not mean they are currently managed by these companies, just that they once were, and that the local staff have proudly kept on running these establishments while awaiting better times to arrive.